The Beauty of Math! These 3D Printed Fractals Will Blow Your Mind

When I was in school, I admittedly was not a fan of mathematics. It was just something about numbers that turned me away. While my grades held up, and I never failed a single math class, I must admit that when I finally graduated, I never missed the subject. However, not everyone feels the same. Mathematics can be fascinating to others, especially when geometric figures called fractals are involved.

Fractals are curves or geometric figures made up of parts which have the same statistical character as the whole. They are mysteriously found in nature as are they in many man-made formations and objects. For one man, named Jérémie Brunet, fractals have always been fascinating.

“Fractals have fascinated me since the 80s when I was a teenager,” Brunet tells 3DPrint.com. “My father offered me a book entitled ‘The beauty of fractals’ which I still cherish to this day. I used to program fractals on my early computers and draw them by hand. About 5 years ago, a new generation of 3D fractals emerged from a collaborative work on fractalforums.com and I became hooked again.”

Image copyright: Coandco

One day, Brunet stumbled upon Shapeways and immediately it became evident that he had to “give physical substance to these strange mathematical creatures.”

“I like to push the boundaries of fractal art, and 3D printing was the perfect technology to that end,” Brunet explains. “To me, they are a way to visualise the beauty of nature, the elegant laws of the universe and the emergence of complexity through simple rules and fundamental ingredients. Today, creating 3D printed fractals still represents many challenges, as these objects bear infinite details by definition, but my passion is to keep on pushing the limits in the 3D fractals domain.”

Currently Brunet has about a hundred different fractals available for various prices on his Shapeways shop. Some are priced at under $10, while others are hundreds of dollars. They range from large plastic 3D prints to smaller pieces of jewelry made of precious metals like gold, silver, and bronze. Brunet relies on Shapeways, opting not to print his designs on desktop FFF-based 3D printers, simply for the fact that those machines can’t provide him with the intricate details needed.

Brunet’s 3D printed fractals (image copyright: Coandco)

“I like to try all the possible colours and materials at my disposal,” he tells us. “I’m sure that one day, affordable and fine resolution metal desktop 3D printers will be available, then I’ll probably invest.”

As for designing his individual fractals, they require a lot of hard work and time. The workflow is complex, involving the exportation of voxel stacks from Mandelbulb3D, which is a freeware fractal generator. The stacks are then combined into a triangle mesh in a process referred to as a “marching cubes” algorithm, and then they are post-processed and optimized in Meshlab. Recently Brunet has begun using another software package called Incendia EX, which provides a special feature that allows exporting directly to STL files.

Brunet tells us that, while he sells quite a few of his fractals on Shapeways, he really has spent more on buying them himself than he has earned through sales. He hopes to break even one of these days, perhaps this year or next. Regardless, his 3D printed fractals are gaining him quite a bit of attention.

“Most recently, one of my sculptures has been shown at the Brown Symposium at Southwestern University in Texas as part of an art exhibit dedicated to 3D printing called ‘What Things May Come‘. Even if this is just a hobby, my next large scale project in 3D printing is to collaborate on the build of a massive 3D printed fractal temple for the Burning Man festival in Nevada, hopefully in 2017. Stay tuned!”

Even though I don’t have an interest in mathematics, like Brunet does, I certainly have an appreciation for the designs that he has created. I may just end up buying a few of his incredible fractals for myself. What do you think about Brunet’s fractals? Have you purchased any yourself? Discuss in the 3D Printed Fractals forum thread on 3DPB.com. Also be sure to check out Brunet’s YouTube channel, as well as some additional photos below.